A Covariant Density Functional Study Of Low-lying States In Neutron-deficient Krypton Isotopes And The Development Of Relativistic Projected Shell Model

The spectroscopy provides an important way to explore and understand the nature of microscopic world. The spectroscopy of nuclear low-lying states contains rich information of nuclear structure and becomes one of the key topics in nuclear physics. In the past decades, nuclear covariant density functional theory (DFT) has achieved great success in the description of nuclear structure and becomes nowadays one of the most important microscopic approaches for systematic studies of ground state properties of nuclei all over the nuclear chart. In recent years, point coupling covariant density functional theory has been widely used to study the low-lying excited states in nuclei by implementing projection method and generate coordinate method or collective Hamiltonian.The research works presented in this thesis are based on the point coupling covariant DFT and are composed of the following two aspects:1) The five-dimensional collective Hamiltonian (5DCH) with parameters determined by the point coupling covariant DFT calculation is used to calculate the low-lying excited states of neutron-deficient krypton isotopes. The results include the potential energy surface, excitation energy and electric multipole transition strength, etc. A good agreement with the experimental data is achieved. We have studied the phenomena of shape evolution and shape coexistence in isotope70-78Kr from the systematic behavior of these quantities as functions of neutron number. The results exhibit a picture of oblate-triaxial-prolate shape transition. There are O2+states with low excitation energies but distinctly different deformations with the ground state in most neutron-deficient Kr isotopes, indicating the shape coexistence in these nuclei. In addition, we have adopted the exact generator coordinate method (GCM) plus particle number projection (PNP) plus angular momentum projection (AMP) method based on the same energy functional to calculate the low-lying excited states in76Kr. By comparing the mean-field results and the beyond mean-field results calculated by the5DCH and the projected GCM, the effects of dynamic correlations and triaxiality on nuclear structure have been examined. These effects turn out to play an important role in reproducing the energy order of oblate and prolate deformed configurations in nuclei around N=40.2) Using the effective Hamiltonian deduced from the point coupling covariant density functional and the wave function including many (quasi-) particle-many (quasi-) hole configuration mixing, we have established the theoretical framework of relativistic projected shell model.